Cold and SotS are definitely songs where you should be alt picking (at least economy picking).

Spirit Crusher wouldn't be impossible to downpick, though I don't know why anyone would do anything except economy/alt pick most of the song.

I don't listen to ABRB at all, but I'm willing to bet that you'd probably want to alt pick something by them too.

EDIT: Honestly I would try to train alt picking as much as possible. It's been a long time since my metal band and I still use alt/econo picking in whatever I'm playing. It just makes your playing so much more dynamic in both rhythm and lead.

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I honestly never heard the difference when playing on single string. Technically, alternate picking would offer more benefit to master.

With a single string it doesn't make much difference. It's in full chords where the two have different sounds, unless you really practice at making them sound the same. (And in any case, it'll never sound EXACTLY the same, because the notes are being hit in a different order).

But anyway, I agree, alternate picking is what TS should master. Downpicking sounds good to emphasize heavy palm-muted chords, but your speed is severely limited. By getting a good alt picking technique, you'll be able to play much faster stuff without tiring.

Plus, the way I see it, if I can alternate pick, then downpicking is a basic, easy skill. The best metal guitarists (and arguably ALL guitarists) use a mix of the two, in appropriate situations.